On bounded paradoxical sets and Lie groups

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-04-14 DOI:10.1007/s10711-024-00923-1

Grzegorz Tomkowicz

引用次数: 0

Abstract

We will prove that any non-empty open set in every complete connected metric space (X, d), where balls have compact closures, contains a paradoxical (uncountable) set relative to a non-supramenable connected Lie group that acts continuously and transitively on X.

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论有界悖论集和李群

我们将证明，在每个完整连通度量空间（X, d）中，球具有紧凑闭合的任何非空开集，都包含一个相对于连续且传递地作用于 X 的非可上推连通李群的悖论（不可数）集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.